The width of a rectangle is 6 less than twice its length. if the area of the rectangle is 110 cm^2, what is the length of the diagonal?

The area of the rectangle is 273 square units.

The task is to find the area of a rectangle where the width of the rectangle is given as 13, and the area as a function of x is provided as A(x) = 2x² - 5x.

To find the area, we need the value of x that corresponds to the width. Since the width is 13, we set x as 13 and substitute it into the area function.

A(13) = 2(13)² - 5(13) = 2(169) - 65 = 338 - 65 = 273 square units.

Thus, the area of the rectangle is 273 square units.

I teach 9 and 6 hours respectively

Left diagram:

In this diagram you show three quarters of the hours.

We have then:

(3/4) * (12) = 9

Answer:

You teach 9 hours.

Right diagram:

In this diagram you teach half of the hours.

We have then:

(2/4) * (12) = 6

Answer:

You teach 6 hours

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You tutored for 6 hours, your friend tutored for 6 hours as well.

Image:

You and a friend listen for a total of 2 hours.

You

Friend

You

The image shows a tape diagram with two sections labeled "You" and "Friend". The "You" section is longer than the "Friend" section, indicating that you tutored for more hours than your friend.

To find the number of hours that you tutored, we can divide the total number of hours tutored (12 hours) by the number of sections in the tape diagram (2).

Number of hours you tutored = 12 hours / 2 sections = 6 hours

Therefore, you tutored for 6 hours.

Explanation of tape diagrams:

A tape diagram is a visual representation of a mathematical equation. It is a horizontal bar that is divided into sections, with each section representing a different quantity. The length of each section represents the size of the quantity it represents.

Tape diagrams can be used to solve a variety of mathematical problems, including addition, subtraction, multiplication, and division problems. They are especially useful for solving problems that involve multiple quantities, as they can help to visualize the relationships between the different quantities.

In this case, the tape diagram is used to solve the following problem:

> You and a friend tutor for a total of 12 hours. Use the tape diagram to find how many hours you tutor.

The tape diagram is divided into two sections, one for you and one for your friend. The length of each section represents the number of hours that each person tutored. Since you tutored for more hours than your friend, the "You" section is longer than the "Friend" section.

To find the number of hours that you tutored, we can divide the total number of hours tutored (12 hours) by the number of sections in the tape diagram (2). This gives us the number of hours that you tutored, which is 6 hours.

Therefore, the answer to the question is "You tutored for 6 hours."

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Answer:

The results could be flawed due to non-response of patients.

Step-by-step explanation:

A doctor's office mails a survey to each of its patients. The results of the survey are based off of the total number of patients. The office is mailing the patients. It is very likely that patients do not read out the survey mail. So, they cannot respond to the survey or a very few patients will respond back. So, option 4th is the correct. The results could be flawed due to non-response of patients.

o to 100 miles per hour

Answer: 70 I just took the test!

Step-by-step explanation:

Answer:

9,800

Step-by-step explanation:

Helen's Shop

60 m x 80 m = 4,800 m2

Parking Lot

Length = 2 × 50 m = 100 m

Area = 50 m × 100 m = 5,000 m2

Final Answer

4,800 m2 + 5,000 m2 = 9,800 m2

A parallelogram is a quadrilateral with four sides. The opposite sides of the parallelogram are equal and parallel.

In the given figure, AB||DC. AD is the transversal, such that:

∠A + ∠D = 180-degrees.

Therefore, ∠A and ∠D are supplementary and their sum is equivalent to 180-degrees.

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The hang out time is 0.875 sec.

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x²(a>0) for an equation to be a quadratic equation. The x² term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term. The numerical values of a, b, and c are often expressed as integral values rather than fractions or decimals.

Given Equation:

h(t) = –16t² + 14t

For the Hangout time we can consider the function h(t)=0

0 =  –16t² + 14t

16t² = 14t

16t= 14

t= 14/16

t= 0.875 sec

Hence, the hang out time is 0.875 sec.

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Final answer:

After converting Cube B's side length to feet, Cube A has a surface area of 294 ft² while Cube B has a surface area of 258.2016 ft², making Cube A the one with the larger surface area.

Explanation:

To determine which cube has the larger surface area, we must work with a common unit of measurement for both cubes. We'll convert Cube B from meters to feet using the conversion factor 3.28 ft/1m.
For Cube A with a side length of 7 feet, the surface area (SA) is calculated by the formula SA = 6 × s² (where 's' is the side length).
SA (Cube A) = 6 × (7 ft)² = 6 × 49 ft² = 294 ft².
For Cube B with a side length of 2 meters, we first convert meters to feet: 2 m × 3.28 ft/m = 6.56 ft. So, the surface area of Cube B becomes:
SA (Cube B) =  6 × (6.56 ft)² = 6 × 43.0336 ft² = 258.2016 ft².
Between Cube A and Cube B, Cube A has the larger surface area.

Answer:

Step-by-step explanation:

2^3)(2^-4) = 2^(3-4) = 2^-1 = 1/2

answer is D.

add exponents and keep the same base.then find the reciprocal and change the sign of the exponent

The rule which describes the translation of the figure is T–3, –2(x, y).

The translation T(x, y) → (x – h, y – k) moves a point (x, y) to a new point (x – h, y – k).

T–3, –2(x, y) moves the point 3 units to the right and 2 units down.

T–3, 2(x, y) moves the point 3 units to the right and 2 units up.

T3, –2(x, y) moves the point 3 units to the left and 2 units down.

T3, 2(x, y) moves the point 3 units to the left and 2 units up.

So the answer is T–3, –2(x, y).

Here is a table that shows the effect of each translation on the point (3, 4):

Original point | Translation | New point

(3, 4) | T–3, –2(x, y) | (0, 2)

(3, 4) | T–3, 2(x, y) | (6, 6)

(3, 4) | T3, –2(x, y) | (6, 2)

(3, 4) | T3, 2(x, y) | (0, 6)

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The two positive consecutive even integers that, when their squares are subtracted, equal 76 are 18 and 20.

In this problem, the two positive consecutive even integers can be represented as x and x+2. The problem states that the difference of their squares is 76, which can be put into the equation (x + 2)^2 - x^2 = 76. By simplifying this equation, we get 4x + 4 = 76. Solving for x, we find that x = 18. Therefore, the two consecutive even integers are 18 and 20.

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A student concluded that the solution of the equation [tex]\sqrt{2x+1}+3 = 0[/tex] is x = 4. The conclusion is true.

Perfect squares are those integers whose square root is an integer.

Let x-a be the closest perfect square less than x,

and let x+b be the closest perfect square more than x, then we get x-a < x < x+b (no perfect square in between x-a and x+b, except possibly x itself).

Then, we get:

[tex]\sqrt{x-a} < \sqrt{x} < \sqrt{x+b}[/tex]

[tex]\sqrt{2x+1}+3 = 0\\\\\sqrt{2x+1}= -3[/tex]

by taking square on both sides we get

[tex](\sqrt{2x+1})^2 = (- 3)^2 \\\\2x+ 1 = 9[/tex]

when x = 4

2(4) + 1

= 9

Thus, the solution of the equation is 4.

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Answer:

C. [tex]\dfrac{1}{(m-4)(m-3)}[/tex]

Step-by-step explanation:

First note that

[tex]m^2-16=(m+4)(m-4) \quad \text {and} \quad m^2-9=(m+3)(m-3)[/tex]

On the other hand, the expression from the question is equivalent to

[tex]\dfrac{m+3}{m^2-16} \cdot \dfrac{m+4}{m^2-9}=\dfrac{m+3}{(m+4)(m-4)}\dfrac{m+4}{(m+3)(m-3)}[/tex]

we cancel the equal terms in the numerator and the denominator and finally we get that our expression is equivalent to

[tex]\dfrac{1}{(m-4)(m-3)}[/tex]